Mathematics and Materials
About this Title
Mark J. Bowick, Syracuse University, Syracuse, NY, David Kinderlehrer, Carnegie Mellon University, Pittsburgh, PA, Govind Menon, Brown University, Providence, RI and Charles Radin, University of Texas at Austin, Austin, TX, Editors
Publication: IAS/Park City Mathematics Series
Publication Year: 2017; Volume 23
ISBNs: 978-1-4704-2919-5 (print); 978-1-4704-3749-7 (online)
MathSciNet review: MR3701347
MSC: Primary 82-06; Secondary 82-01
Articles in this volume are based on lectures presented at the Park City summer school on “Mathematics and Materials” in July 2014. The central theme is a description of material behavior that is rooted in statistical mechanics. While many presentations of mathematical problems in materials science begin with continuum mechanics, this volume takes an alternate approach. All the lectures present unique pedagogical introductions to the rich variety of material behavior that emerges from the interplay of geometry and statistical mechanics. The topics include the order-disorder transition in many geometric models of materials including nonlinear elasticity, sphere packings, granular materials, liquid crystals, and the emerging field of synthetic self-assembly. Several lectures touch on discrete geometry (especially packing) and statistical mechanics.
The problems discussed in this book have an immediate mathematical appeal and are of increasing importance in applications, but are not as widely known as they should be to mathematicians interested in materials science. The volume will be of interest to graduate students and researchers in analysis and partial differential equations, continuum mechanics, condensed matter physics, discrete geometry, and mathematical physics.
Graduate students and researchers interested in mathematical aspects of material sciences.
Table of Contents
- Veit Elser – Three lectures on statistical mechanics
- Henry Cohn – Packing, coding, and ground states
- Alpha Lee and Daan Frenkel – Entropy, probability and packing
- Michael Brenner – Ideas about self assembly
- P. Palffy-Muhoray, M. Pevnyi, E. Virga and X. Zheng – The effects of particle shape in orientationally ordered soft materials
- Roman Kotecký – Statistical mechanics and nonlinear elasticity
- Peter Bella, Arianna Giunti and Felix Otto – Quantitative stochastic homogenization: Local control of homogenization error through corrector